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BigPicture is a project management and portfolio management app for Jira environment. First released in 2014 and developed by SoftwarePlant (now by AppFire), it delivers tools for project managers that the core Jira lacks, i.e. roadmap, a Gantt chart, Scope (work breakdown structure), risks, resources and teams modules.
In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972. [1] It says: If k complete graphs , each having exactly k vertices, have the property that every pair of complete graphs has at most one shared vertex, then the union ...
Jira (/ ˈ dʒ iː r ə / JEE-rə) [4] is a proprietary product developed by Atlassian that allows bug tracking, issue tracking and agile project management.Jira is used by a large number of clients and users globally for project, time, requirements, task, bug, change, code, test, release, sprint management.
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
The problem of edge coloring has also been studied in the distributed model. Panconesi & Rizzi (2001) achieve a (2Δ − 1)-coloring in O(Δ + log * n) time in this model. The lower bound for distributed vertex coloring due to Linial (1992) applies to the distributed edge coloring problem as well.
It is named after Michael O. Albertson, a professor at Smith College, who stated it as a conjecture in 2007; [1] it is one of his many conjectures in graph coloring theory. [2] The conjecture states that, among all graphs requiring n {\displaystyle n} colors, the complete graph K n {\displaystyle K_{n}} is the one with the smallest crossing number.
A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color. A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has
The De Bruijn–Erdős theorem also applies directly to hypergraph coloring problems, where one requires that each hyperedge have vertices of more than one color. As for graphs, a hypergraph has a k {\displaystyle k} -coloring if and only if each of its finite sub-hypergraphs has a k {\displaystyle k} -coloring. [ 20 ]